## Differential Equations and Their Applications: An Introduction to Applied MathematicsMathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as weil as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high Ievel of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. T AM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Seiences ( AMS) series, which will focus on advanced textbooks and research Ievel monographs. Preface to the Fourth Edition There are two major changes in the Fourth Edition of Differential Equations and Their Applications. The first concerns the computer programs in this text. In keeping with recent trends in computer science, we have replaced all the APL programs with Pascal and C programs. The Pascal programs appear in the text in place ofthe APL programs, where they are followed by the Fortran programs, while the C programs appear in Appendix C. |

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### Contents

1 | |

Second order linear differential equations 2 | 127 |

Systems of differential equations 3 | 264 |

Qualitative theory of differential equations 4 | 372 |

Separation of variables and Fourier series 5 | 476 |

SturmLiouville boundary value problems 6 | 514 |

Appendix A | 545 |

Appendix B | 547 |

Appendix C | 549 |

### Other editions - View all

Differential Equations and Their Applications: An Introduction to Applied ... Martin Braun No preview available - 1994 |

Differential Equations and Their Applications: An Introduction to Applied ... Martin Braun No preview available - 2014 |

### Common terms and phrases

addition approaches infinity approximate assume called coefficients columns complex compute Consequently Consider constant continuous converges cost curve defined Definition denote dependent derivative determine differential equation dy/dt eigenvalues eigenvectors elements equal equilibrium solution Example Exercise exists Figure force function given gives glucose Hence homogeneous implies increasing initial initial-value problem integral interval Laplace transform Lemma limit linear linearly independent matrix method Moreover multiply negative observe obtain operator orbit partial particular period polynomial population positive Program PROOF Property prove region remain Remark respectively roots satisfies Section Show sides simple sint solution x(t solve space species stable Suppose system of equations term Theorem tion unique vector verify write zero